We start by studying whether cooperation can ever be favored on fully directed networks, which contain no bidirectional edges. To consider this problem we first recall the key intuition used in prior studies to explain why bidirectional population structures can favor cooperation. In that setting, once a cooperator disperses her strategy to a neighbor, she will benefit from reciprocity in the next generation, receiving donations from her neighbor. By contrast, if a defector disperses his strategy to a neighbor, he will suffer in the next generation and receive nothing from his neighbor.
Thus, the formation of `cooperator clusters' and `defector clusters' favors the evolution of cooperation in bidirectional networks [1]}, [2]}, [3]}.
